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Lecturer(s)
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Loukotová Lucie, Mgr.
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Bazaykin Yaroslav, doc. CSc., DSc.
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Course content
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1. Parametric equations of curves (circle, conic sections, helix, cycloids) 2. Tangent and osculating plane of curves 3. Length of arc, arc of curve as parameter 4. Frenets formulas, curvature and torsion 5. Osculating circle 6. Parametric equations of surfaces (sphere, quadrics, torus) 7. Curves on surfaces, tangent plane, first fundamentals form 8. Second fundamental form, asymptotic and principal directions 9. Asymptotic curves and lines of curvature on the surface 10. Geodesic curves 11. Surfaces of revolution 12. Ruled surfaces (developable, warped surfaces) 13. Cartographic mappings
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Geometry and differential (integral) Calculus is used to study curves (cycloids, helix) and surfaces (ruled surfaces, surfaces of revolution). Frenet-formulas for curves, the osculating plane and osculating circle are presented. The course is also devoted to important curves on the surface (asymptotic curves, lines of curvature and geodesic curves). Mean and Gaussian curvature and cartographic mappings are introduced.
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Prerequisites
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unspecified
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Assessment methods and criteria
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unspecified
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Recommended literature
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Boček L., Kubát V. Diferenciální geometrie křivek a ploch, SPN, Praha, 1983.
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Budinský B. Analytická a diferenciální geometrie, SNTL, Praha, 1983.
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